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trap101
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Test Tomorrow...Help!...Fermat's Little Theroem
Prove that if "p" is an odd prime, then
a) 1p-1+2p-1+...+(p-1)p-1 "is congruent" to -1(mod p)
attempt: Well I know from Fermat's little theorem, that all the constants on the left hand side will reduce to 1's:
1 + 1 + 1...1 (is congruent to) -1 (mod p).
I know there is just a small step to conclude this, but I can't figure it out.
b) 1p+2p+...+(p-1)p (congruent to) 0 (mod p) (Hint: it may be useful to show: 1+2+...+(p-1) = p(p-1) / 2
Kinda lost with this one sad thing is I got help with it today...smh.
Prove that if "p" is an odd prime, then
a) 1p-1+2p-1+...+(p-1)p-1 "is congruent" to -1(mod p)
attempt: Well I know from Fermat's little theorem, that all the constants on the left hand side will reduce to 1's:
1 + 1 + 1...1 (is congruent to) -1 (mod p).
I know there is just a small step to conclude this, but I can't figure it out.
b) 1p+2p+...+(p-1)p (congruent to) 0 (mod p) (Hint: it may be useful to show: 1+2+...+(p-1) = p(p-1) / 2
Kinda lost with this one sad thing is I got help with it today...smh.